The state laws require a lot of specialized teachers in private schools once you get above elementary. Not a problem when you have a couple hundred students, but if you're starting a new school, expecting an initial enrollment of 50, it's tough to have the specialists for every subject. Our local Catholic school just started going through High School a couple years ago, after they had grown so much that they had to double the size of their elementary school. The School Board here is strongly opposed to competition. They've had a couple lawsuits filed against them for denying Charter School charters. A couple were for schools that were already certified PA Charter Schools in other parts of PA, but somehow didn't meet the criteria here. They are more concerned about the 'financial losses' from allowing charter schools than anything else.
I see. In an area with a high density of private schools and a good highway network, you can have the specialists part-time in a number of schools, being at School A on Mondays, School B on Tuesdays, etc. If you stagger school hours a bit, you might even be able to have a few public high school teachers moonlight at the private school, scooting over at the end of the public school day to teach a class at last period in the private school